Question

solve the system of equations. state the decimal solution to the nearest hundredth.
$3.45x + 5.13y = 8.39$
$5.21x + 0.26y = 9.34$
approximately ( , )
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Explanation:

Step1: Isolate y in Eq2

From $5.21x + 0.26y = 9.34$, rearrange to solve for $y$:
$0.26y = 9.34 - 5.21x$
$y = \frac{9.34 - 5.21x}{0.26}$

Step2: Substitute y into Eq1

Substitute $y = \frac{9.34 - 5.21x}{0.26}$ into $3.45x + 5.13y = 8.39$:
$3.45x + 5.13\times\frac{9.34 - 5.21x}{0.26} = 8.39$

Step3: Simplify to solve for x

First calculate $5.13\div0.26\approx19.7308$:
$3.45x + 19.7308(9.34 - 5.21x) = 8.39$
Expand: $3.45x + 184.2857 - 102.7975x = 8.39$
Combine like terms: $-99.3475x = 8.39 - 184.2857$
$-99.3475x = -175.8957$
$x = \frac{-175.8957}{-99.3475}\approx1.77$

Step4: Calculate y with x≈1.77

Substitute $x\approx1.77$ into $y = \frac{9.34 - 5.21x}{0.26}$:
$y = \frac{9.34 - 5.21\times1.77}{0.26}$
Calculate $5.21\times1.77\approx9.2217$:
$y = \frac{9.34 - 9.2217}{0.26} = \frac{0.1183}{0.26}\approx0.45$

Answer:

$(1.77, 0.45)$